Math Forum - Problem of the Week

Counterfeit Coins

The Math Genie appears while you are doing your math homework. He offers you a small pouch of nine coins.

"What's the catch?" you say.

He tells you, "Eight of these are rare and quite valuable. One of them is a counterfeit. It weighs more than the other coins. I've brought this old two-pan balance. If you can find the counterfeit in the minimum number of weighings possible, the coins are yours."

Question: What's the fewest number of weighings that will identify the counterfeit coin for certain? Describe the steps you would take and how you can be confident you have found the counterfeit.

Extra: Describe the fewest number of weighings it would take to find the counterfeit if you did not know whether it was lighter or heavier.

Use this Java applet from the National Library of Virtual Manipulatives to help you think about the: Coin Problem